Get a Straight Answer

    I'm 40 years old and passed my junior high and High school and I never understood Algebra, the substitution and replacement rules for the "X" or "Y's"

    When I accessed your page I thought it was just another informative science page, but I'm so surprised by the way how you explain the formulas Off course this came to me about 35 or so many years late but still enjoyable, I really appreciate this small gift that you gave me on this night.

    I will definitely introduce this page to my daughters I'm sure they will really appreciate it too.

    Please keep up your excellent job

Victor

By the way I read the Spanish version
(English spelling and wording were corrected)

...and more:

I'm 32 years-old Mexican living in Mexico.
        Please receive this quick note to thank you for setting up a web page on the Pythagoras' Theorema, but specially for your infinite kindness of providing a Spanish translation.

    I just stumble with the fact that I don't remember my high school math. And I needed it to deduct the measurement for 2 hypothenuses that are part of a sculpture (a triangular prism) of which I'm writing a paper on. After some web-surfing I got directed to your page. And... problem solved, I was able to get the paper written with its right measurements.

Again, thanks sharing your knowledge.
        Rosina

...still more (Spanish, though not math):

    I have just visited your website and am so excited that I found something in Spanish! I teach Integrated Physics and Chemistry at Pampa High School, Pampa, Texas. Every year I have students who are ESL and have very little or no understanding of English, I have been trying to find some resources on Lab Safety and metric measurements in Spanish. I like what you have on your site, but it is not appropriate for these students. Do you know of any resources on the internet in Spanish that I could use as a supplement to my lessons. I would appreciate any information that you could give me.

Thank you ... Diana

...and still more (math, from Africa):

    I accessed the site containing (M-1)Algebra--the basic ideas and it appears to be the stuff that I need to familiarize myself with. I want to write the GMAT exam for MBA, for the 2nd time. Last was in May 2001 and my score was rather dismal. My math knowledge is minimal, and I realize that math in fact seems to be fun. If the basic idea is to isolate all that one does not need in the process of solving a problem and remain with what one needs on both sides, geez, I do wish I had known this ages back. I just hope I will be able to figure out all that you explain.

After visiting NASA solar sailing page I saw your name as a reference.

    Do you know who validated solar pressure? Did anybody actually measure the pressure a (hefty) laser puts on a mirror? Michelson measured the speed of light but did anybody actually measure light's pressure?

Reply

    Light pressure was predicted by Maxwell's theory of electromagnetic waves. It was verified in 1910 by the Russian physicist Pyort Nikolaevich Lebedev. See

Hello Professor Stern,

    I came along to your site regarding seasons while researching a question - How do scientists approximate the time (down to the minute) that seasons change? Can you answer this question or point me in the right direction to find the answer.

Reply

Dear Christiana

    During the year, the Sun seems to follow a large circle around the sky, among the "fixed" stars which define the constellations and whose positions are essentially fixed, because they are so far. That circle is known as the ecliptic, and is described on the web site.

    Because of the Earth's rotation, the sphere of stars also seems to rotate. It has two "poles" around which the rotation takes place, one in the northern half of the sky and the other in the southern half. The first is visible only north of the equator, the second only south of it. The line halfway between the poles is knows as the equator of the celestial sphere, or the celestial equator. This, too, is described in the first sections of "Stargazers".

    These two circles--the ecliptic and the celestial equator--intersect (as any two circles on a sphere must do, if each divides the sphere in two equal halves). The seasons are defined somewhat arbitrarily by this geometry. The two points of intersection are the spring and fall equinox, and when the Sun is there, night and day are equal (hence the name). The first is viewed as the start of spring,: see story on the Persian New Year in the section on the calendar, in the yellow box there. The second is the start of fall, around September 23.

    Summer starts when the Sun is as far north of the ecliptic as it can get--that is the summer solstice, around June 21, the longest day. And winter starts when the Sun is as far south as it can get, and that is when nights are longest, around December 21.

I am really confused on how the accelerator grids function [in ion rockets]. I know that the negative grid accelerates the ions out of the ionization chamber but what exactly does the positive grid do? Does it act as a decelerator or as a repulsive force for the positive xenon ions? Are both grids on at the same time? How do the positive xenon ions get past the positive grid? Does one grid have a higher potential than the other?

    I have been to many websites and I have read that the ions are accelerated as the result of "the potential difference between the grids"... what does this mean?

    Any clarification will be greatly, greatly appreciated.

Reply

"Potential" is a mathematical term also known colloquially as "voltage" because its value is measured in units called "volts." It is somewhat like height in a gravity field: a stone falls from a high location to a low one, and gains energy in proportion to the height difference it crosses. A proton or a positive xenon ion "falls" from high potential to low potential, and gains energy.

    One difference: there also exist negative particles, like electrons, for whom "up" and "down" are reversed. Electrons gain energy moving from low potential (very negative) to high potential (very positive). Except for this reversal, everything is similar.

Still with me?

    So we have two parallel grids, positive (say) on top and negative on bottom. The space in between is where electric forces can be observed, and a region like that is known as "electric field." Electrons released in this space move up (TO the high voltage), positive ions like those of xenon move down (AWAY FROM high voltage).

OK?

    I truly enjoyed your web page on librations of the moon.

You wrote:

"In addition to the preceding modes, there also exist "physical" librations, actual pendulum-like nodding and wobbling of the Moon around its equilibrium position, like the spring-attached head of one of those "bobblehead dolls" popular as souvenirs. The main mode is pole-to-pole nodding and amounts to about a degree and a half. The longitudinal side-to-side oscillation, on the other hand, has an amplitude of only a quarter of a minute of arc, much too small to be measured by ordinary telescope-based methods. It can however be quite easily checked by laser signals bounced back from the sets of reflecting prisms left by Apollo 11, 14 and 15 astronauts on the Moon, part of the ALSEP or "Apollo Lunar Surface Experiment Package," or by the set placed there by the Soviet Luna 21 robot lander. The results are in agreement with the theory of such motions, which was extended to cover motions previously neglected as unobservable."

I would be very interested to learn the following:

1. What are the periods of these two modes of oscillations?

2. Are these oscillations damped? If so, what is the damping time constant? Or the data collected cover to short an observation period to make any conclusions about the damping?

Reply

Dear Mik

    I think my claim about physical librations came from the book by Cook, cited at the end of my web page on librations. I am away from the library now, so instead I made a quick check on the web. Here is what I found at

A dumb question from a retired engineer (ex NERVA program)

(the NERVA rocket was an experimental nuclear rocket in the early days of space research)

    The de Laval nozzle has an expanding portion. One wonders how the exhausted propellant can impart any force on this section after it has already left the nozzle throat.

"There aint anything for the gas to push against!"

    The expanding gas delivers--I suppose-a hydrostatic pressure in all directions, and a component of the force on the nozzle helps push the rocket.

    I guess this is a non-problem based on naive physics. None of the propellant has anything to "push against" after all.

Reply

    Your question ain't dumb (and didn't NERVA have a De-Laval nozzle?).

    You can look at the situation in one of two ways. One, the "bell" of the nozzle looks like a paraboloid, and the exit from the narrow section is near its focus. Hot molecules coming from it can be viewed like rays of light emitted from a flashlight bulb, hitting the flashlight reflector and bouncing off, all into directions parallel to its axis.

    OK, there exist many collisions on the way.. so look in another way at what happens when the jet comes out from the narrow section. The hot gas expands outwards, cools by expansion and loses heat energy. The heat energy goes into expansion velocity, which after hitting the "bell" is all rerouted parallel to the axis. The thrust is exerted against the bell. Is that what you meant?

    Of course, rigorous calculations also exist. I'm just trying to make the result plausible.

Response:

Yes, the NERVA rocket did have a De Laval nozzle. We even did a thrust measurement with a down-firing reactor, in Nevada air.

David,

    I have been perplexed for years on why the Space Shuttle rotates during liftoff at initial flight stage. I can not find the answer anywhere I have searched or read on this subject. I have asked many people and no one has a clue why this maneuver takes place. I have sifted through reams of documents on space flight and this fact is never discussed. It is probably some simple reason.

I am talking about shortly after liftoff the shuttle rotates. Why?

    I am a computer specialist with a large Computer company. I have a pilots license and have been flying for over thirty years. I am knowledgeable about flying and I a an avid flying enthusiast. I would be forever grateful if you could answer this elusive question.

Reply

    Dear Ed

    I have not paid that much attention to shuttle lift-offs, and don't know the answer. But I looked on the web, and an answer DOES exist there. See:

I am most interested in Cold Fusion. Do there exist any in-depth websites you can recommend for this subject?

Reply

Cold fusion is not my area of expertise, but I can recommend a "Wikipedia" article at

Hello Dr. Stern

    I'm dong a bit of research for a Science Fiction novel I'm writing. While I realize that one can take great liberties with such things, I prefer to stay (in some situations) as close to "fact" as I can.

    To this end, I was wondering if you could outline, in a very broad sense obviously, what effect a collision between a neutron star and our sun would have.

    If this fictional neutron star were moving at a good clip, could it pass right through, ripping our poor sol's guts out? (So to speak!) Would the sun implode? Explode? Would the added mass convert the Neutron star into a black hole? How long would these processes take? Would a near miss pull mass/gas from the sun causing it to cool?

    What I need for this to work out (for me, not the poor people in the book) is for the sun to "cool" or even be extinguished, but relatively gradually over several months at least, though a year would be better, to a point that would render the planet very, very cold and uninhabitable.

    Thanks for any reply/time you can lend to this project.

Reply

Dear Chris

    Luckily, I do not have to think too hard about your questions, because someone has already done it for me. Try to get hold of the "Scientific American" of November 2002, and look up the article "When Stars Collide." which is also featured (with a snazzy illustration) on the cover. Yes, the collision with a neutron star could lead to a black hole or just to a more massive neutron star. The results to humanity would be devastating and abrupt.

    You look for a scenario that would be less abrupt, and I am not really an astrophysicist. On the other hand, science fiction is less constraining than science (and I exclude here fantasy, where anything goes). Namely, in science you have to prove that your claim is probably correct, while in science fiction it is enough to make it hard to prove it wrong (and being just improbable is not disqualifying).

    So maybe you could have a star of some sort (may be a white dwarf, which allows an interesting transition) pass close enough--maybe strike the Sun peripherally--to tear off a good fraction of its mass, say 10%-20%, and carry it away. The remaining Sun would be smaller and therefore dimmer. I leave it to you to figure out details.

    There exists an old Sci-Fi book "The Black Cloud" by Fred Hoyle. Hoyle's literary merits are less impressive than his scientific ones (at least, some of those), but "Black Cloud" is probably his best (and first). A dark cloud approaches the Sun and envelops it, dimming it temporarily (though ultimately sunlight must get through). But the cloud stops at the Sun and does not go flying on, because (as it turns out), it's intelligent and can control its own motion. I write this to point out that a dark cloud may not be the solution you look for, but read Hoyle anyway, he has some interesting views on the ups and downs of climate in such circumstances, e.g. the role of humidity.

Response

I can't thank you enough for pointing me in the right direction. Unfortunately a white dwarf is a little too visible for my purposes, so I guess I will have to take some liberties somewhere. Not too much as I grew up on such authors as Robert Heinlein, Ben Bova and Robert L. Forward. (Who wrote a truly remarkable book about life evolving on a Neutron star, "Dragon's Egg") All of whom tried their best to stick to known science where ever possible.

Again, thanks for the help!

My 3 year old wants to know why the moon looked red on Aug 1. Can you help me answer her question?

Reply

Dear Pat

    Hard to answer without more information! It's like asking a doctor over the telephone why does my back hurt. There can be many answers. The doctor needs to know more.

    My guess, though, is that the moon was near the horizon. It's the air, and dust in the air, and water droplets, which change the color, and moonlight coming from near the horizon goes through the greatest thickness of air. The sun also looks red near the horizon--more on some days, when the air has more matter floating in it. Such as smog. little droplets collected by exhaust from cars and machinery.

Dr. Stern

    I am involved in planning a human centrifuge for the International Space Station or for exploration missions.

    Several folks have proposed using a short-arm human centrifuge. Correct me if I am wrong, but doesn't the g-force get less as you move toward the center of the radius? In other words, if I have an astronaut seat in a chair in a 1.6 meter radius centrifuge, and he gets one g at his feet, but wouldn't his head get something like .5 g?

    It would appear to me, based on equations and mathematical models, that the larger the centrifuge, the less dynamic change across someone standing on the centrifuge. If I have a large 10 meter centrifuge, the distance from the center of the radius to my head is much greater, and the change in g from my feet to my head less.

    Now here is where things get a little complicated. What is I put two centrifuges together but in opposite directions. For instance lets say I have a centrifuge that is 6 meters in radius turning in a clockwise direction, and then just inside that centrifuge (perhaps on a layer of ball-bearings) I have another centrifuge that is say 5.95 meters in radius and turning in the opposite counterclockwise direction. Would the G force be additive? If they are at the same speed, would the net movement of someone on the dual centrifuge be zero?

Reply

Centrifuges are not my area, and I am not sure to what uses they are put, What you say about centrifuges is correct, but of course persons whirled around in a centrifuge do not keep their legs and heads at different radial distances. Rather, they tend to keep their spine parallel to the axis of rotation--like those riders inside a whirling drum in amusement park rides. On such persons the force is more or less uniform--like the force on an astronaut lying flat on a couch in an accelerating spacecraft during launch.

    There may, though, exist Coriolis forces on the flow inside blood vessels. I do not know how important that is, but it may get more pronounced in a short-arm centrifuge. That is your field, not mine.

    What you propose, counter-rotating centrifuges inside each other, will not work--the motions will subtract, because they must be considered in the frame of the non-rotating universe. (Handling a counter-rotating circular motion inside a rotating frame takes more math, but presumably leads to the same result). The problem is discussed on my web site

Thanks so much! That was very helpful. As you are aware, we are looking at both short-arm and long-arm centrifuges for exploration. The Coriolis effect on the neurovestibular system will indeed be a problem with the short-arm centrifuge, but the vehicle torques (to say nothing of the expense, upmass, and volume) would be a problem with the long-arm centrifuge.

    I appreciate the insight. I was not sure how to calculate a counter-rotating centrifuge, or whether the forces would be additive or subtracting, or would simply negate one another. I had the picture of Stanley Kubrick's "2001: A Space Odyssey" centrifuge in my mind

    What force holds galaxies together? I mean, Pluto alone is barely clinging on to the edge of our motley bunch of planets... the nearest star is over 4 light years away and I'd bet its not feeling a great deal of attraction to us gravitationally at least, and yet stars are clustered together in galaxies. Is there another force at work here? Something that we can't yet measure? Or can we measure it, and know about it, and the only reason it is not well known is that it hasn't been publicized as much?
Thanks for your time,

Reply

    I'm a retired mathematician/computer scientist, now mentoring some students on Science Fair projects at Presentation High School, San Jose CA. I've just been reading your interesting article: "Can an Astronaut on Mars distinguish Earth from its Moon?" at Pumas web site

    I would like to know if the view of the moon shape is the same from each different point of the earth in the same moment or if it changes depending on the different geographic places from we are observing the moon from the earth. I have studied History of Art and haven't read too much about astronomy; also I haven't found information about this issue.

Reply

    In the last few months, I have noticed that each night, after the Moon passes its greatest distance from the horizon, it appears to rotate clockwise approx. 90 degrees. That is a LOT of rotation!

    In other words, when the Moon is highest above the horizon, the crater Tycho, (for example), is at the 5 o'clock position on the moon's face, (as is normally expected and pictured) but within the space of just several hours it rotates to nearly the 8 O'clock position. No new or additional surface of the moon is revealed, just a rotation of what was already visible. This seemingly odd occurrence is easily visible to anyone who cares to look up.

    What is up with such a thing? I don't recall that ever occurring before. Am I just not getting enough sleep?

Initial Reply:

    I have a question to ask you! I am 16 yrs old and for my astronomy class, I was given an assignment to measure the altitude of the tip of the handle of the Big Dipper. But I am having a little problem with trying to get an answer. Any ideas, suggestions or help from you will be appreciated.

Reply:

    It is a strange assignment, to say the least, because the altitude of the tail star of the Big Dipper changes all the time. As you should know, the sky appears to rotate around a fixed spot, the pole of the sky, which now happens to be very close to the star Polaris.

    (If you don't realize that, stop here and read the first 3 sections for "From Stargazers to Starships.")

    The tail star of the Big Dipper thus follows a circle around the pole star, taking about 24 hours for a full circuit. Its altitude--its distance from the horizon--will depend on the position in that circle where you find it.

    Let me instead suggest you measure two other angles: the altitude of the pole star (which should equal your geographical latitude--see those sections of "Stargazers")--and the angle between the tail star of the Big Dipper and the pole star (see the flag of Alaska in section #1-c, which has both those stars near the top of the flag.

    That measurement tells you the radius of the circle in which the tail star moves, while the first measurement tells you the altitude of the center of the circle. Add them to get the highest altitude of the tail star, subtract to get the lowest (if negative, it's then below the horizon), and other information can also be obtained.

    You can use a telescope, and from the declination of the tail star you can find the radius, in degrees. A telescope can also tell you the altitude at any time, although you need some calculations. Or you can build a simple cross-staff like the one in section #5-B, except you can use simpler sights, because you will perform only two measurements.

    I am a therapist at a home for fourteen abused teenaged boys. As part of their therapy they are given problems for them, as a group, to solve. A recent problem, which has generated a lot of discussion goes as follows -

    A rocket ship is returning to Earth after a flight to the moon. Various things happen on the journey forcing the boys to make difficult decisions: like putting a crew member out of the airlock into space. This particular problem ended with the crew, as they reached 5 miles high running out of breathable air. What would happen if the crew opened the air lock at this point?

        Would the cabin fill with air, and the ship continue to descend without problems?
        Would the ship become uncontrollable and crash?
        Would the crew roast in the heat from the engines?

Or would something totally different happen? If you have any enlightening thoughts on the problem, we wait with bated breath to hear them.

Reply:

    What a question! At 5 miles, the air is very cold and has about 1/3 of the seal-level density. You could breathe it, but might get unconscious after a while from lack of oxygen. The question is really, how bad is the air you are breathing at this point. It probably has much more oxygen, but build-up of carbon dioxide may befuddle your mind. I don't know what to recommend, but waiting a little longer seems best.

    Will the ship crash? At that point, it is probably no longer guided by its passengers. It may be descending by parachute (like moon-return capsule) or gliding down on stubby wings like the space shuttle. Opening a door will make no difference. Engines are no longer active--fuel is so precious in rocket flight that all of it is used going up.

    There exists a similar question, more practical. You are flying in an airliner at 5 miles (a reasonable altitude) and suddenly a poorly secured hatch flies open. Or else, a bomb was carried aboard, and it blows a hole in the side of the cabin. What happens next?

    Such things have taken place, and by all accounts they are terrifying. The air whooshes out, and if you are (say) a stewardess standing in the aisle, you may be flung to your death, though passengers strapped into their seats are likely to stay there. A moderately small hole will just cause a very rapid drop in pressure, the air will expand and cool, and since cabin air is fairly humid, the cabin will immediately fill with fog. As emergency instructions tell you, oxygen masks will automatically drop down from bins in the ceiling, helping you breathe more easily, while the pilots frantically descend to denser air.

    A real big rupture could damage the integrity of the airplane. If the passenger cabin decompresses much faster than the cargo space below, or vice versa, the floor may buckle, for instance. A Turkish airliner crashed near Paris, many years ago, because a poorly secured cargo bay door came off in flight. None of the 300-odd passengers survived.

    Maybe the next problem to your group will be of a happier sort!